Home/Chain Registry/Block #192,527

Block #192,527

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/3/2013, 10:38:44 PM · Difficulty 9.8745 · 6,608,858 confirmations

TWN

Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header

Block Hash

cb27d7a5d189be8b5f3f5867a44ebb3da244a37f29d55a4872c92d0364ff48a9

View on Chainz ↗

Height

#192,527

Difficulty

9.874458

Transactions

Size

656 B

Version

Bits

09dfdc83

Nonce

5,949

Timestamp

10/3/2013, 10:38:44 PM

Confirmations

6,608,858

Merkle Root

db7af8f761722783d4a483b758f50edbce2b5448ad189d78fb41e39f05e2356e

Transactions (3)

Coinbasef50741ba1dd8d9…536416275c596e

1 in → 1 out10.2600 XPM110 B

ANvtpRa1…QjsraDJz

7e41253ac598ce…3feb2c48426997

1 in → 2 out10.2300 XPM226 B

AMqLGXtK…yS2mEEdL AJhgf59P…W42GoeAR

0b8ec7af9556c6…e1ade9dadb1e33

1 in → 2 out6.1544 XPM227 B

ATspUaQm…ZgArVNra AMmGeXac…8N1iWEtv

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

7.184 × 10¹⁰²(103-digit number)

71848985558195267282…16000084924398453760

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 — Twin Prime Pair (origin ± 1)

origin − 1

7.184 × 10¹⁰²(103-digit number)

71848985558195267282…16000084924398453759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.184 × 10¹⁰²(103-digit number)

71848985558195267282…16000084924398453761

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

1.436 × 10¹⁰³(104-digit number)

14369797111639053456…32000169848796907519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.436 × 10¹⁰³(104-digit number)

14369797111639053456…32000169848796907521

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

2.873 × 10¹⁰³(104-digit number)

28739594223278106913…64000339697593815039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.873 × 10¹⁰³(104-digit number)

28739594223278106913…64000339697593815041

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

5.747 × 10¹⁰³(104-digit number)

57479188446556213826…28000679395187630079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.747 × 10¹⁰³(104-digit number)

57479188446556213826…28000679395187630081

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

1.149 × 10¹⁰⁴(105-digit number)

11495837689311242765…56001358790375260159

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

View full Prime Chain Discovery page →

★☆☆☆☆

Rarity

CommonChain length 9

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial − 1 and p+2 = origin/primorial + 1

Verify on a Primecoin Node

Anyone running a Primecoin node can independently verify this block using the following RPC commands. Run these from the primecoin-cli command line or via the debug console in the Primecoin wallet.

1. Get block hash by height

getblockhash 192527

Returns the block hash for a given block height. Use this to confirm the hash shown above matches the chain.

2. Get full block data

getblock cb27d7a5d189be8b5f3f5867a44ebb3da244a37f29d55a4872c92d0364ff48a9

Returns the full block header including difficulty, prime chain origin, prime chain type, transaction IDs, and all other fields shown on this page.

How to run these commands: To verify this data independently, open a terminal on your own Primecoin node and run primecoin-cli <command>. Alternatively, open the Primecoin-Qt wallet, go to Help → Debug Window → Console, and type the command directly. The node must be fully synced to this block height for the commands to return results.

Cross-reference on Chainz Explorer

Chainz is an independent Primecoin block explorer. Compare this block's data to verify accuracy.

View Block #192,527 on Chainz ↗